Question

if sin theta = -1/3 and theta does not lies in the third quadrant then cos theta = ?​

Answer 1

Step-by-step explanation:

sinθ=−

3

1

=>sin

2

θ=

9

1

sin

2

θ+cos

2

θ=1

9

1

+cos

2

θ=1

cos

2

θ=1−

9

1

=

9

8

cosθ=±

9

8

=±

3

2

2

=>cosθ=

3

2

2

orcosθ=−

3

2

2

Now sinθ is negative, θ must lie in 3rd or 4th quadrant.

But it is given that θ does not lie in 3rd quadrant..

So θ lies in 4th quadrant

In 4th quadrant cosθ is positive.

=>cosθ=−

3

2

2

=>cosθ=

3

2

2

Ans=

3

2

2